In a blistering six-minute period at the start of the second half, Harry Kane scored three goals - including a penalty that led to Ireland defender Liam Scales being sent off after receiving a second caution. Anthony Gordon and Conor Gallagher also notched their first international goals during this incredible display, leaving the visitors shell-shocked.
Jarrod Bowen soon added a fourth with his first touch after coming on as a substitute, before Taylor Harwood-Bellis headed home a fifth as a third player got off the mark for the Three Lions.
Ireland had initially done an excellent job to largely frustrate England in a feisty first half that ended with Carsley's side having 75 per cent possession, but without having tested visiting goalkeeper Caoimhin Kelleher.
So much so that England tempers boiled over on the stroke of half-time as Kane and Jayson Molumby squared up to each other, with both players booked as Heimir Halgrimsson's team deservedly went in level at the break.
TrendingThings could possibly have gone even better for Ireland, already sure of third place in the group, had two penalty appeals gone their way. However, Belgian referee Erik Lambrechts waved away both appeals and those incidents were soon forgotten as England finally made the breakthrough eight minutes after the break.
Kane's inch-perfect, raking cross-field pass found Jude Bellingham in space in the box, with Scales only able to bring the midfielder down with his trailing leg as he cut back inside to shoot. The Celtic defenders earned a second booking for his troubles - his first was delaying a re-start - and Kane easily sent Kelleher the wrong way from the spot for his 69th international goal.
Minutes later, England doubled their advantage after a mix-up in the visitors' defence allowed Tino Livramento to centre for Gordon to stylishly volley home at the back post, before Gallagher tapped in after Marc Guehi had nodded on Noni Madueke's corner.
Harshly for Ireland, the goals kept on coming in the final quarter of an hour as Bowen swept home with his very touch after coming on following a cleverly-worked corer routine, and then fellow substitute Harwood-Bellis rose well to guide Angel Gomes' cross back past a helpless Kelleher.
As a result Carsley - described as "top drawer" by Kane after the game - achieved the objective set out to him by The Football Association when he took temporary charge of the team in August by guiding them back to League A of the Nations League.
England boss Lee Carsley to ITV:
"I wanted the England team to be exciting to watch, be attacking. I see them day in, day out on the training ground and now people have seen it.
"It's given the staff and myself the confidence we can do the job. You always doubt yourself, whether you could do it or not.
"There's a lot of England managers sat in the house picking the team, and to have the responsibility to do that and the trust from my bosses has been a massive boost of confidence.
"I think it was a good performance. The way we started the game, we played with real intent and it was frustrating to come off 0-0 at half-time, but I believed that we'd score goals if we just kept doing what we spoke about. It was great we got our rewards in the end.
"It was a great evening for a lot of the players. The main thing was getting promotion, what we set out to do, so it was pleasing in that respect."
Republic of Ireland manager Heimir Hallgrimsson:
"I'm lost for words. Six minutes of madness. It was a shock, conceding a penalty, conceding a goal, losing a player. We lost our heads at that moment, leading into the second and third goals.
"It's easy to sit and criticise on the sideline. After the first half, coming in, it's a game like we wanted it to be. We defended compact, they didn't find ways to play through us.
"Conceding so early in the second half, losing a player, conceding another two, it's easy to criticise - it's normal, but excuses when you lose 5-0 are pathetic. It's embarrassing."
Roy Keane on ITV:
"If you listen to some of his [Thomas Tuchel] media stuff, I think that seems to suit him. I think he likes the idea of maybe getting in for a couple of years and that's his target - knockout football. I think it kind of suits his personality.
"England have got some brilliant, talented players. It's his job just to try and bring it all together. But the next World Cup will be different, because of the conditions and the heat.
"For a lot of these brilliant young players, they've got to stay grounded. There's pitfalls ahead for some of them but if they've got good people around them, stay grounded, keep working hard, then they'll have an impact at the World Cup."
England turn their attention to the World Cup qualifying draw on December 13.
All eight Nations League quarter-finalists are in Pot 1 of the World Cup draw, which will be completed by the four countries with the best FIFA world ranking.
England and Belgium are guaranteed to take Pot 1 slots as they are ranked fourth and sixth in the world respectively. As it stands, Switzerland and Austria will take the other two Pot 1 places.